Plurisubharmonic Functions on Affine Line Bundles over Compact Kähler Manifolds

Abstract

We investigate function-theoretic properties of holomorphic affine line bundles over compact Kähler manifolds. We discuss existence of (strictly) plurisubharmonic functions on the total space of such a bundle. Further, we give a precise restriction from below on the growth of such functions. This gives refinements of some previous results due to one of the present authors. In the proof, we construct a plurisubharmonic exhaustion function satisfying the Monge–Ampère equation and look at the foliation induced by this function.